Projectiles Question -- Tiger Woods drives a golf ball on the Moon

AI Thread Summary
Tiger Woods drives a golf ball on the Moon at a speed of 285 km/h and an angle of 42 degrees, resulting in a calculated horizontal distance of 3.9 km. The discussion highlights the importance of converting units from km/h to m/s and correctly applying the gravitational acceleration of 1.60 m/s² on the Moon. Participants clarify the time of flight and horizontal distance calculations, emphasizing the need to consider vertical and horizontal components separately. Misunderstandings about gravity's role in the equations are addressed, leading to corrections in calculations. Ultimately, the correct distance is confirmed as 3.9 km based on proper application of physics principles.
rr96
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Homework Statement



As part of a NASA experiment, golfer Tiger Woods drives a golf ball on the moon, where
g = 1.60 m/s2. He ‘launches’ a golf ball with a speed of 285 km/h, at an angle of 42o with the horizontal. What horizontal distance will his drive travel before landing back on the surface of the moon. Ignore the curvature of the moon.

Homework Equations



d = (Vi)(t) + 1/2(a)t2

Vf =Vi + at

(Vf)2 = (Vi)2 + 2ad

The Attempt at a Solution



Initial horizontal velocity:

285 x cos42
= 211.8 km/h

Initial Vertical Velocity

285 x sin42
= 190.7 km/h

Finding time using vertical components

d = (Vi)(t) + 1/2(a)t2

0 = 190.7t - 4.9t2

t = 38.9 s

Using time to find distance

d = (Vi)(t) + 1/2(a)t2

d = 211.8 x 38.9 + 1/2(0)t2

d = 8239 m
 
Last edited by a moderator:
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rr96 said:
0 = 190.7t - 4.9t2
4.9?
 
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Sorry, I skipped a step. 1/2 x 9.8 = 4.9
 
rr96 said:
Sorry, I skipped a step. 1/2 x 9.8 = 4.9

Haruspex is a smart guy, I'm sure he could see the step you skipped.

His next question would be:

"9.8?"
 
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Besides that, though, there's one more small problem. Your units are inconsistent.

(You need to convert km/hr to meters/second)
 
Thanks! I completely missed that. My final answer is 635 m
 
rr96 said:
Thanks! I completely missed that. My final answer is 635 m

My answer disagrees.

How long will the ball be in the air? (What was your calculation for this?)
 
10.8 s ?
 
Last edited:
d = (Vi)(t) + 1/2(a)t2

0 = 52.97t - 4.9t2

t = 10.8 s
 
  • #10
Have you forgotten where this is taking place? :) Remember, we're not on Earth.
 
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  • #11
d = (Vi)(t) + 1/2(a)t2

0 = 52.97t - 0.8t2

t = 66.21 s

I had forgotten! Thank you so much!
 
  • #12
Final answer is 3.9 km
 
  • #13
There you go, that should be the correct answer.

(Do you have something that says what the correct answer is?)
 
  • #14
Yup! That's what it says the answer is.
 
  • #15
You have missed out on crucial piece of information which the value of is 1.60m/s^2 as the event is taking place on the moon
 
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  • #16
rr96 said:
Final answer is 3.9 km

Can you explain how you got this? I followed the replies and tried doing it myself but don't understand at all how you're getting to 3.9
 
  • #17
hr14 said:
Can you explain how you got this? I followed the replies and tried doing it myself but don't understand at all how you're getting to 3.9
What do you get and why?
 
  • #18
PeroK said:
What do you get and why?
This is what I did...

vx: 285 x cos42
= 211.8 km/h = 58.83 m/s

vy: 285 x sin42
= 190.7 km/h = 52.97 m/s

d = (Vi)(t) + 1/2(a)t2
0 = 52.97t - 0.8t2
t = 66.2125s

d = (Vi)(t) + 1/2(a)t2
d = 58.83 x 66.2125 + 1/2(1.6)(66.2125)2
d = 388 m

388m = 0.388km
 
  • #19
hr14 said:
d = (Vi)(t) + 1/2(a)t2
d = 58.83 x 66.2125 + 1/2(1.6)(66.2125)2
Gravity acts diagonally on the moon?!
But that expression gives 7402m.
I've played around with variants of the above expression for d (ignoring the quadratic term, making it negative) and none lead to 388.
 
  • #20
haruspex said:
Gravity acts diagonally on the moon?!
But that expression gives 7402m.
I've played around with variants of the above expression for d (ignoring the quadratic term, making it negative) and none lead to 388.
I tried again and did get 7402m but converting that to km doesn't give 3.9km (which is the correct answer).
I meant to put a negative sign instead of positive. But doing (-) instead of (+) should give 388
 
  • #21
hr14 said:
I tried again and did get 7402m but converting that to km doesn't give 3.9km (which is the correct answer).
I meant to put a negative sign instead of positive. But doing (-) instead of (+) should give 388
You seem to have overlooked my rhetorical question:
haruspex said:
Gravity acts diagonally on the moon?!
 
  • #22
haruspex said:
You seem to have overlooked my rhetorical question:
No, it doesn't. It acts vertically
 
  • #23
hr14 said:
No, it doesn't. It acts vertically
So why do you have a gravity term in the horizontal displacement equation?
hr14 said:
d = (Vi)(t) + 1/2(a)t2
d = 58.83 x 66.2125 + 1/2(1.6)(66.2125)2
 
  • #24
haruspex said:
So why do you have a gravity term in the horizontal displacement equation?
I figured it out. Thanks
 
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